City entered the match trailing the previously unbeaten Reds by seven points, but fine finishes from both Sergio Aguero and Leroy Sane helped the club to a vital victory that closed the gap on the league leaders to just four points.
Jurgen Klopp’s Reds had opened up their lead in the league following a down month of December for the defending Premier League champions, who lost matches to Chelsea, Leicester City and Crystal Palace in the final month of 2018.
“We had a chance and opportunity to show our quality after a couple of bad results,” he told the club’s website.
“We’re back on track and on winning ways.
“The team has been playing good games and this is the most important for us. If you play bad you can win the games, but you have to play good and get the three points.
“It was a nice game for everybody and of course for the fans. They were so excited, and I am happy for them.”
The match saw Roberto Firmino pull Liverpool level just after the hour mark only to see Sane hit a superb winner eight minutes later.
Fernandinho put in a fine showing in his own right and says the tension of high-stakes matches leaves no room for error.
“I think all the big games are like this [tense]. You cannot blink. You get punished, all the games are high tension, so you have to be careful all the time and everyone who was involved had the same feeling, the same sensation.”
City will have to wait a bit before getting another chance to close the gap on Liverpool.
The club return to the pitch on Sunday with an FA Cup clash against Rotherhamand face a Carabao Cup semi-final first-leg with Burton on Wednesday before returning to Premier League action against Wolves on January 14.